We extend the multinomial logit model to represent some of the empirical phenomena that are frequently observed in the choices made by humans. These phenomena include the similarity effect, the attraction effect, and the compromise effect. We formally quantify the strength of these phenomena that can be represented by our choice model, which illuminates the flexibility of our choice model. We then show that our choice model can be represented as a restricted Boltzmann machine and that its parameters can be learned effectively from data. Our numerical experiments with real data of human choices suggest that we can train our choice model in such a way that it represents the typical phenomena of choice.
Travel providers such as airlines and on-line travel agents are becoming more and more interested in understanding how passengers choose among alternative itineraries when searching for flights. This knowledge helps them better display and adapt their offer, taking into account market conditions and customer needs. Some common applications are not only filtering and sorting alternatives, but also changing certain attributes in real-time (e.g., changing the price). In this paper, we concentrate with the problem of modeling air passenger choices of flight itineraries. This problem has historically been tackled using classical Discrete Choice Modelling techniques. Traditional statistical approaches, in particular the Multinomial Logit model (MNL), is widely used in industrial applications due to its simplicity and general good performance. However, MNL models present several shortcomings and assumptions that might not hold in real applications. To overcome these difficulties, we present a new choice model based on Pointer Networks. Given an input sequence, this type of deep neural architecture combines Recurrent Neural Networks with the Attention Mechanism to learn the conditional probability of an output whose values correspond to positions in an input sequence. Therefore, given a sequence of different alternatives presented to a customer, the model can learn to point to the one most likely to be chosen by the customer. The proposed method was evaluated on a real dataset that combines on-line user search logs and airline flight bookings. Experimental results show that the proposed model outperforms the traditional MNL model on several metrics.
The dynamic Boltzmann machine (DyBM) has been proposed as a stochastic generative model of multi-dimensional time series, with an exact, learning rule that maximizes the log-likelihood of a given time series. The DyBM, however, is defined only for binary valued data, without any nonlinear hidden units. Here, in our first contribution, we extend the DyBM to deal with real valued data. We present a formulation called Gaussian DyBM, that can be seen as an extension of a vector autoregressive (VAR) model. This uses, in addition to standard (explanatory) variables, components that captures long term dependencies in the time series. In our second contribution, we extend the Gaussian DyBM model with a recurrent neural network (RNN) that controls the bias input to the DyBM units. We derive a stochastic gradient update rule such that, the output weights from the RNN can also be trained online along with other DyBM parameters. Furthermore, this acts as nonlinear hidden layer extending the capacity of DyBM and allows it to model nonlinear components in a given time-series. Numerical experiments with synthetic datasets show that the RNN-Gaussian DyBM improves predictive accuracy upon standard VAR by up to 35%. On real multi-dimensional time-series prediction, consisting of high nonlinearity and non-stationarity, we demonstrate that this nonlinear DyBM model achieves significant improvement upon state of the art baseline methods like VAR and long short-term memory (LSTM) networks at a reduced computational cost.
Thanks to the availability of large scale digital datasets and massive amounts of computational power, deep learning algorithms can learn representations of data by exploiting multiple levels of abstraction. These machine learning methods have greatly improved the state-of-the-art in many challenging cognitive tasks, such as visual object recognition, speech processing, natural language understanding and automatic translation. In particular, one class of deep learning models, known as deep belief networks, can discover intricate statistical structure in large data sets in a completely unsupervised fashion, by learning a generative model of the data using Hebbian-like learning mechanisms. Although these self-organizing systems can be conveniently formalized within the framework of statistical mechanics, their internal functioning remains opaque, because their emergent dynamics cannot be solved analytically. In this article we propose to study deep belief networks using techniques commonly employed in the study of complex networks, in order to gain some insights into the structural and functional properties of the computational graph resulting from the learning process.
We have some algorithm that's given a handful of labeled examples, say 10 images of dogs with the label 1 ("Dog") and 10 images of other things with the label 0 ("Not dog")--note that we're mainly sticking to supervised, binary classification for this post. The algorithm "learns" to identify images of dogs and, when fed a new image, hopes to produce the correct label (1 if it's an image of a dog, and 0 otherwise). We have some algorithm that's given a handful of labeled examples, say 10 images of dogs with the label 1 ("Dog") and 10 images of other things with the label 0 ("Not dog")--note that we're mainly sticking to supervised, binary classification for this post. The algorithm "learns" to identify images of dogs and, when fed a new image, hopes to produce the correct label (1 if it's an image of a dog, and 0 otherwise). This setting is incredibly general: your data could be symptoms and your labels illnesses; or your data could be images of handwritten characters and your labels the actual characters they represent.